WASHINGTON—A few days after President Donald Trump gave his Pentagon chief the unilateral authority last month to send thousands of American troops to Afghanistan at his own discretion, the White House sent classified guidance that effectively limits the number of forces.

The memo, sent by national security adviser Lt. Gen. H.R. McMaster to a small group of administration officials, said that the president would let Defense Secretary Jim Mattis send no more than 3,900 troops to Afghanistan without coming back to confer with...